What is x^2-5|x|+6<0 ?

The solution to x^2-5|x|+6<0 is -3<x<-2\lor 2<x<3

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x^2-5|x|+6<0

x^{2} - 5 ∣ x ∣ + 6 < 0

- 3 < x < - 2 or 2 < x < 3

Solution steps

x^{2} - 5 ∣ x ∣ + 6 < 0

Find positive and negative intervals

x < 0, x \geq 0

Solve the inequality for each interval

- 3 < x < - 2 or 2 < x < 3

\frac{( 3 x )}{( x ^{2} - 4 )} \leq 1

∣ 5 x ∣ < ∣ 10 - 5 x ∣

x^{2} - 3 x + ∣ x + 1 ∣ \geq 4

\frac{( x - 4 )}{( x + 2 )} \leq \frac{( x - 2 )}{( x - 1 )}

x^{2} + x - 6 < 6